This paper considers the problem of learning Chinese word embeddings. In contrast to English, a Chinese word is usually composed of characters, and most of the characters themselves can be further divided into components such as radicals. While characters and radicals contain rich information and are capable of indicating semantic meanings of words, they have not been fully exploited by existing word embedding methods. In this work, we propose multi-granularity embedding (MGE) for Chinese words. The key idea is to make full use of such word-character-radical composition, and enrich word embeddings by further incorporating finer-grained semantics from characters and radicals. Quantitative evaluation demonstrates the superiority of MGE in word similarity computation and analogical reasoning. Qualitative analysis further shows its capability to identify finer-grained semantic meanings of words.